It is the nature of sensors that they react on real impacts with a certain time lag. Especially, this is true in fast varying environments in which the quantity to be measured may change in form of a step function, for example. However, the corresponding sensor signal may not step up to the new real measure value but rather gets there with a certain response time.
There are many applications that only work properly with a sensor supplying a fast response to fast varying measures. However, for many sensors there are limitations in modifying the hardware in order to improve the response time.